Math Problem Statement

If x≥ 0 and y > 0 are real numbers, simplify the following expression

If x ≥ 0 and y > 0 are real numbers, simplify the following expression.

Solution

The expression in the image appears to be:

72x6,x0\frac{\sqrt{72x}}{6}, \quad x \geq 0

To simplify this:

Step 1: Simplify the square root

The number inside the square root, 72, can be factored into 72=36×272 = 36 \times 2, and since 36 is a perfect square, we can simplify it:

72x=36×2x=62x\sqrt{72x} = \sqrt{36 \times 2x} = 6\sqrt{2x}

Step 2: Substitute into the original expression

Now substitute 62x6\sqrt{2x} into the expression:

62x6\frac{6\sqrt{2x}}{6}

Step 3: Simplify the expression

The 6's cancel out, so you are left with:

2x\sqrt{2x}

Thus, the simplified expression is:

2x\boxed{\sqrt{2x}}

Would you like more details or have any questions? Here are five related questions for further exploration:

  1. How do you simplify square roots of non-perfect squares?
  2. What is the general process for simplifying radical expressions involving variables?
  3. Can you apply this simplification to any other similar expressions involving different numbers?
  4. What are the conditions under which the square root function is defined?
  5. How does this simplification help in solving equations involving radicals?

Tip: Always look for perfect square factors inside the square root to simplify the expression easily.

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Math Problem Analysis

Mathematical Concepts

Algebra
Radicals
Simplification

Formulas

\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}

Theorems

Simplification of square roots
Properties of radicals

Suitable Grade Level

Grades 9-11